Rees short exact sequences and preenvelopes

Abstract In this paper, we consider some properties of commutative diagrams of Rees short exact sequences, and we also investigate the sufficient and necessary condition under which the induced sequences by functors − ⊗ M for the left S -act M . The main conclusions extend some known results. Further, we investigate preenvelopes and precovers in the category 𝓔 S of Rees short exact sequences of right S -acts.